1、Yunnan University,A History of Computer Science and Technology,Fall 2007,Dr. Tong Li,Chapter 1,The Digital Enters into the Mans Life,1.1 Decimal System,The number system we use on a day-to-day basis is the decimal system, which is based on ten digits: zero through nine. The name decimal comes from t

2、he Latin decimal meaning ten, while the symbols we use to represent these digits arrived in Europe around the thirteenth century from the Arabs who, in turn, acquired them from the Hindus.,As the decimal system is based on ten digits, it is said to be base-10 or radix-10, where the term radix comes

3、from the Latin word meaning root . Outside of specialist requirements such as computing, base-10 numbering systems have been adopted almost universally. This is almost certainly due to the fact that we happen to have ten fingers. (including our thumbs). If mother nature had decreed six fingers on ea

4、ch hand we would probably be using a base-twelve numbering system.,1.2 Carving Notches Into Bones 30,000 BC to 20,000 BC,The first tools used as aids to calculation were almost certainly mans own fingers, and it is not simply a coincidence that the word digit is used to refer to a finger (or toe) as

5、 well as a numerical quantity.,How to Represent Larger Numbers ?,As the need to represent larger numbers grew, early man employed readily available materials for the purpose. Small stones could be used to represent larger numbers than fingers and toes, and had the added advantage of being able to ea

6、sily store intermediate results for later use. Thus, it is also no coincidence that the word calculate is derived from the Latin word for stone.,Cro-Magnon Mans Bones,The oldest known objects used to represent numbers are bones with notches(槽口) carved into them. These bones, which were discovered in

7、 western Europe, date from the Aurignacian（舊石器時(shí)期） period 20,000 to 30,000 years ago and correspond to the first appearance of Cro-Magnon man. (The term Cro-Magnon comes from caves of the same name in Southern France, in which the first skeletons of this race were discovered in 1868.),The Tally Syste

8、m,Of special interest is a wolfs jawbone(鄂骨) more than 20,000 years old with fifty-five notches in groups of five. This bone, which was discovered in Czechoslovakia（捷克斯洛伐克） in 1937, is the first evidence of the tally（計(jì)算） system. The tally system is still used to the present day, and could therefore

9、qualify as one of the most enduring of human inventions,The first evidence of the tally system.,The Discovery of Prime Numbers,Also of interest is a piece of bone dating from around 8,500 BC, which was discovered in Africa, and which appears to have notches representing the prime numbers 11, 13, 17,

10、 and 19. What is surprising is that someone of that era had the mathematical sophistication to recognize this quite advanced concept and took the trouble to write it down - not the least that prime numbers had little relevance to everyday problems of gathering food and staying alive.,1.3 The First P

11、lace-Value Number System -1900BC,The decimal system is a place-value system, which means that the value of a particular digit depends both on the digit itself and on its position within the number. For example, a four in the right-hand column simply means four . in the next column it means forty . o

12、ne more column over means four-hundred . then four thousand, and so on.,Sexagesimal Numbering System,For many arithmetic operations, the use of a number system whose base is wholly divisible by many numbers. And so we come to the Babylonians, who were famous for their astrological (占星術(shù)) observations

13、 and calculations, and who used a sexagesimal (base-60) numbering system. Although sixty may appear to be a large value to have as a base, it does convey certain advantages. Sixty is the smallest number that can be wholly divided by two, three, four, five, and six . and of course it can also be divi

14、ded by ten, fifteen, twenty, and thirty. In addition to using base sixty, the Babylonians also made use six and ten as sub-bases.,Although the Babylonians sexagesimal system may seem unwieldy（笨拙的） to us, one cannot help but feel that it was an improvement on the Sumerians（閃族人） who came before them.

15、The Sumerians had three distinct counting systems to keep track of land, produce, and animals, and they used a completely different set of symbols for each system!,1.4 The Shamanistic Tradition,The start of the modern science that we call “Computer Science” can be traced back to a long ago age where

16、 man still dwelled in caves or in the forest, and lived in groups for protection and survival from the harsher（粗糙的） elements on the Earth. Many of these groups possessed some primitive form of animistic religion（萬(wàn)物有靈論）; they worshipped the sun, the moon, the trees, or sacred （神圣的） animals. In order

17、to correctly hold the ceremonies to ensure good harvest in the fall and fertility（肥沃） in the spring, the shamans needed to be able to count the days or to track the seasons. From the shamanistic tradition, man developed the first primitive counting mechanisms - counting notches on sticks or marks on

18、 walls.,1.5 A Primitive Calendar,From the caves and the forests, man slowly evolved and built structures such as Stonehenge（巨石柱）. Stonehenge, which lies 13km north of Salisbury, England, is believed to have been an ancient form of calendar designed to capture the light from the summer solstice in a specific fash